Remark 5.2 
The classical statistic \(Z_n\)  is normalized in the sense that \(\mathbb {E}Z_n=0\)  and \(\mathop {\mathrm {Var}}Z_n=1\) . The \(t\) -statistic is not normalized (see [1]}). In general, the self-normalized sum is also not normalized (see r.E-Tn2). If \(X_1\)  is symmetric however, it is normalized because
\(\mathbb {E}T_n=\mathbb {E}\Big [\widetilde{\mathbb {E}}\big [ S_n/V_n \big ]\Big ]=\mathbb {E}\Big [V_n^{-1}\sum \widetilde{\mathbb {E}}\big [ X_j \big ] \Big ]=0\) 
